HEAT, MOISTURE, AND MOMENTUM BUDGETS
FOR AN
OKLAHOMA SQU4L LINE
by
JUDITH STOKES
B.A., Clark College of the Atlanta University Center
1974
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF MASTER OF
SCIENCE
at the
MASSACHUSETTS fNSTITUTE OF
TECHNOLOGY
JUNE, 1976
Signature of Author.
.
.
.
.
.
)
Department Af Meteorology, May 7, 1976
Certified
by........-.
....-......
.
Accepted by. . . . . . . . . . . . . . . . . . . .
Chairman, Departmental Committee
WITHO&WN
NCoo%
Heat, Moisture, and Momentum Budgets
for an
Oklahoma Squall Line
by
Judith Stokes
Submitted to the Department of Meteorology on May 7, 1976, in partial
fulfillment of the requirements for the degree of Master of Science.
ABSTRACT
A squall line, which passed through the National Severe Storms
Laboratory mesonetwork in Oklahoma on 26 April 1969, is analyzed to
determine the interaction between cumulus elements and the mean mesoscale atmosphere, by examining the mesoscale circulation and obtaining
cumulus effects as residuals in the budgets of heat, moisture, and
momentum. The analyses are based on data from 23 rawinsonde ascents to
the 400-mb level, 29 automatically surface recording stations, and radar
PPI coverage.
The squall-line thunderstorms first appeared behind a surface cold
front, formed a uniform line, and then moved out ahead of the front.
Analysis of the surface data showed that the surface wind shift and
the temperature break associated with the gust front had a curve-shaped
pattern and these two events were overtaken by the onset of rain in the
northern part of the network.
A composite analysis of all the data revealed the existence of a
mesoscale downdraft-updraft doublet in the vertical motions pattern.
The downdraft is centered at about 10 km ahead of the leading edge of
the radar echo line and the updraft centered at about 5 km behind the
line. The downdraft appears to be driven by evaporative cooling from
the tops of cumulus clouds and cooling due to the dissipation of a middle
cloud layer; the updraft is driven by condensational heating and superimposed convection.
On the basis of this and other cases it is tentatively concluded
that this doublet of mesoscale vertical motions may be a distinguishing
feature of large convective storm systems in their mature stages of
developement whether they be of frontal or of squall-line character.
Thesis Supervisor:
Frederick Sanders
Title: Professor of Meteorology
TABLE OF CONTENTS
Page
ABSTRACT......
.......... . . . . . . . . . .
TABLE OF CONTENTS. . . . . .
. - - - - - - -.
. . . . . .
- - -. .
LIST OF ILLUSTRATIONS . . . . . . . . . . . . . .
1. Introduction. . . . . . . . . . . . .-.
.. .
2
. . .
........
3
4
.
. . . . . . . . . .. .
.
6
2. Description of the 1969 NSSL mesonetwork and data. . . . . . .
.
8
3. Synoptic-scale situation. . . . . . . . . . . . . . .. . . . . . .
4. Mesoscale situation and organization of data. . . . . . -.
5. Distribution of meteorological variables. . . . .
a. horizontal wind components. . .
- - - ....
.. . .
9
-. .
13
.. . .
18
.... . .. ..
b. divergence and vertical wind component . . . . . . . . . .
18
.
19
c. mixing ratio. . . . . . . . . . . . . . . . . . . . . . . . . 23
d. equivalent-potential temperature.
... .
.........
e. potential temperature . . . . . . . . . . . . . . . .
6. Mesoscale budgets. . -. .
25
.. .
26
- - - - - - - - - - - - - - - -.-.-.-. 27
a. discussion of concepts . . . .
.-
- - - - - - - - -..
.27
-
b. equivalent-potential temperature. . . . . . . . . . . . . ..
28
c. potential temperature. . . . . . . . . . . . . . . . . . . .
29
d. mixing ratio. . . . . . . . . . . . . . . . . . . . . . . . .
29
e. v - momentum
. . . . ..
30
.. .
32
..
......... . . . . . . .
7. Concluding remarks .. . . . .
.. . . .
. . . .. . .
.. .
ACKNOWLEDGEMENTS. . . . . . . . . . . . . . . . . . . . . . . . . . .
35
APPENDIX . ...-. . . . . . . . .
36
REFERENCES. .a
.....
---.-.-.-.-.-.-.-.-.-.-.-.-.-.-..
...... . ..
. .... . . ......
38
TABLE 1. WSR-57 Video Contour Levels and Equivalent Reflectivities .
40
FIGURE LEGENDS . . . . . . . . . . . . . . . . . . .
41
. .
.
. .
.
ILLUSTRATIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
LIST OF ILLUSTRATIONS
Figure
Page
1
The 1969 NSSL upper-air and surface mesonetwork. . . . . .
44
2a
Surface synoptic analysis at 0600 CST, 26 April 1969. . . .
45
2b
400-mb analysis at 0600 CST, 26 April 1969. . . . . . . ..
. 46
3a
Tinker Air Force Base sounding at 0600 CST, 26 April 1969
47
3b
Tinker Air Force Base sounding at 1800 CST, 26 April 1969
.48
4
Surface synoptic analysis at 0600 CST, 27 April 1969. ....
5
Surface maps over the state of Oklahoma on 26 April 1969
at 0900, 1200, 1500, and 1800 CST. . . . . . . . . . . . . . 50
6
Radar PPI displays
a. 0900 CST. . .
b. 1200 CST. . .
c. 1500 CST. . .
d. 1800 CST . . .
7
8
9
.
.
.
.
at
.
.
.
.
0
.
.
.
.
49
deg elevation
. . . . . . . . . . . . . . . . . . .51
. . . . . . . . . . . . . . . . . . 52
. . . . . . . . . . . . . . . . . . 53
......
..........
54
Temperature and rainfall traces recorded at automatic
surface recording station, 2C . . . . . . . . . . . . .
.
55
Isochrones of first temperature break and isochrones of
leading edge of radar echoes. . . . . . . . . . . . . . . .
Isochrones of first westerly component in wind direction
.
56
.
57
10
Isochrones of onset of rain. . . . . . . . . . . . . . . . . 58
11
Isohyets
12
Radar PPI displays at
a. 1600 CST. . . . .
b. 1630 CST. . .. .
c; 1700 CST. . . . .
13
Isochrones of LERE line, radar PPI display at 0 deg
elevation at 1650 CST, and the adopted coordinate system.
63
Vertical cross-section display of balloon trajectories
and radar echoes. . .. . . . . . . . . o . . . . . . . . .
64
15
U component of the wind. . . . . . . . . . . . . . . . . .
65
16
V component of the wind. . . . . . . . - - . . . . . . -.
66
17
Divergence of horizontal wind field. . . . . . . . . . . .
67
14
of total amount of rainfall on 26 April 1969.
0
.
.
.
deg
. .
. .
. .
.
.
59
elevation
. . . . . . . . . . . . . . . . 60
. . .
.
. . . . . . . . . . . . 61
. . . . . . . . . . . . . . . . 62
Page
Figure
18
Surface divergence pattern at 1640 CST. . . . . . . . . . .
68
19
Profile of domain-averaged vertical motion. . . . . . . . .
69
20
Mesoscale vertical motions. . . . . . . . . . . . . . . . .
70
21
Mesoscale mixing ratio, streamfunction lines of flow, and
relative humidity areas less than 25% and greater than 75% . 71
22
Mesoscale equivalent-potential temperature and streamfunction lines of flow. . . . . . . . . . . . . . . . . . . . .
72
Mesoscale potential temperature and streamfunction lines
.
of flow. . . . . . . . . . . . . . . . . . . . . - . .
73
23
Approximate apparent source of equivalent-potential temperature . . . . . . . . . . .
. 74
Approximate apparent source of equivalent-potential temperature minus u transport . .
- 75
25a
Approximate apparent source of potential temperature. . .
. 76
25b
Approximate apparent source of potential temperature
. . . . . . . . . . . . - - 77
minus u transport. . . . . . .
24a
24b
26a
Approximate apparent source of mixing ratio. . . . . . . . . 78
26b
Approximate apparent source of mixing ratio minus u
transport . . . . . . ... ..
Observed surface rainfall rate. . . . .. .....
. .
....
.-
79
80
Coriolis force plus paramaterized surface friction force
(in the lowest layer) per unit mass. . . . . . . . . . .
81
Approximate mesoscale v - accelerations. . . . . . . . .
82
.
1.
Introduction
Some weather systems are too small to be followed in the standard
synoptic network, yet produce profound results.
Such organized systems
as squall lines, masses of thunderstorms, sea-breeze systems, and large
precipitation cells are in this category.
They are said to be mesoscale
phenomena (Byers, 1974).
Since the establishment of the rawinsonde mesonetwork at the National
Severe Storms Laboratory (NSSL) in Oklahoma in 1966, it has been possible
to study the mesoscale aspects of convective storm systems using a large
number of vertical soundings together with a recording surface network,
instrumented aircraft, and radar surveillance.
Barnes et al. (1971)
describe the archived soundings at NSSL for the years 1966 through 1970.
Some'recent studies have made use of the NSSL rawinsonde data.
Lewis et al. (1974) analyzed a case to determine the synoptic-scale influence
upon squall-line generation.
Fankhauser (1974) examined the squall-line
case of 8 June 1966 to derive horizontal height perturbations dynamically
consistent with mesoscale wind patterns in the presence of a well-organized
squall line.
The most intensive use of the NSSL rawinsonde data was made
by Sanders and Paine (1975), hereafter referred to as S & P.
Their exami-
nation of a frontal disturbance was directed toward studying the interaction between cumulus elements and the mesoscale pattern of motion.
Little research has been directed toward the study of the interaction of
these two scales.
Most studies have been concerned with the effects of tro-
pical convection upon the synoptic scales (Yanai et al., 1973; Ogura and
Cho, 1973).
The present examination of the 26 April 1969 squall-line case
(documented at NSSL) is addressed to the interaction between cumulus elements
and the mean mesoscale atmosphere,by determining the mesoscale circulation
and obtaining the cumulus effects
as residuals in the budgets of heat,
moisture, and momentum.
On 26 April 1969 a squall line formed in the vicinity of a slow
moving cold front in northwestern Oklahoma.
The line strengthened during
the day and moved east-southeastward ahead of the front through the 2700
square-kilometer mesonetwork area of NSSL.
During the squall line's
passage through the network much data was.assembled, including observations
from 29 automatically recording surface stations, vertical soundings from
29 rawinsonde ascents, and Plan Position Indicator (PPI). radar coverage
at elevations from 0 to 18 deg.
This storm system can be classified as
severe, since it produced hail of up to 1.75 inches in diameter and
spawned one known tornado.
Presented in the following sections are the description of the 1969
NSSL mesonetwork and data, the synoptic-scale events associated with the
storm system, the results of analysis performed on mesoscale data, and
the results of budget calculations.
8
2. Description of the 1969 NSSL mesonetwork and data
The 1969 NSSL mesonetwork is shown in Fig. 1. The surface network
consisted of 29 stations with a mean spacing of about 8 km.
These auto-
matically recorded wind, temperature, irelative humidity, pressure, and
rainfall on strip charts and the sites were battery-powered to prevent
loss of data during commerical power outages
(Barnes et al., 1971).
Eight rawinsonde sites, indicated by darkened circles in Fig. 1, operated
in 1969.
Soundings usually terminated at 400 mb.
For this case 29 sound-
ings were launched over a time period from 1400 to 1755 CST.
soundings, 23 were actually used in the study.
Of these
Unfortunately only 16 of
the remaining 23 had complete data from the surface up to 400 mb.
Radar coverage was provided by a modified WSR-57 10 cm radar at the
NSSL headquarters, surface station 5E.
Following electronic processing,
power received from precipitation is.displayed in range-azimuth coordinates
on a PPI.
Boundaries between two shades of gray and black (echo cancel-
lation) depict constant reflectivity contours.
These values, for even-
numbered frames on the radar film, are given in Table 1 along with the
coded values that are used in this paper (Zittel, 1976).
For odd-numbered
frames the reflectivity values are increased by 5 dBz and the coded values
are increased by .5. Continuous PPI coverage is available from 0800 to
1815 CST for the 26 April case.
The elevation angle is normally zero
but a'n automatic sequence can be initialized at regular intervals in which
the elevation angle is increased by 1 or 2 deg on each sweep to a maximum
elevation angle of 18 deg.
tion angle returns to zero.
Following the highest elevated sweep the eleva-
3.
Synoptic-scale situation
Figure 2 shows the synoptic weather pattern for 0600 CST, 26 April
1969.
In the surface analysis a cold front, associated with a closed
low in the Dakotas, extends southwestward into nor-thwestern Oklahoma and
northern Texas.
Ahead of the front the low-level flow is generally from
the south-southeast, and is transporting warm moist air from the Gulf of
Mexico into the northern Texas-central Oklahoma region.
The 400-mb analysis shows a deep short-wave trough extending from
North Dakota southwestward into New Mexico.
NSSL is located in a position
between upper-level trough and downstream ridge, in a region of strong
southwesterly flow.
This location indicates synoptic-scale ascent is
occurring over NSSL.
The soundings taken at Tinker Air Force Base (near the eastern edge
of NSSL) on April 26, show that conditions were favorable for convective
activity.
The morning and afternoon temperature and dew-point soundings
are illustrated in Fig. 3. At 0600 CST the-soundings reveal a moist layer
from 950 up to 850 mb.
Within the layer the equivalent-potential tempera-
ture is uniformly near 325 deg
K. This moist layer is surmonted by a
dry potentially unstable layer that extends to 750 mb, above which the
temperature distribution of the air column as a whole indicates conditional
instability.
Note the considerable amount of vertical wind shear and veer-
ing of the winds with height.
All these conditions are favorable for
severe convective activity (Fawbush et al., 1951; Browning, 1964).
By 1800 CST heavy thunderstorms and frequent lightning were reported.
The temperature and dew-point soundings indicate an extremely moist layer
from 950 up to 700 mb.
than earlier.
The vertical wind shear is somewhat more pronounced
The surface analysis 24 hours later (Fig. 4) shows that the front
has advanced about 220km, indicating an average rate of advance of about
9 km hr~1.
There is evidence of a squall line in the warm trough ahead
of the front in central Texas, where the wind shift from south-southeast
to northwest is distinct and some stations are reporting heavy thunderstorms.
An examination of the hourly reports from regular surface weather
stations in Oklahoma and the radar film show that the thunderstorm activity on 26 April had become well organized into a line by 1500 CST.
The
formation of this line, its position relative to the surface front, and
hourly surface synoptic-scale weather was investigated by reviewing a
sequence of three-hourly surface maps (prepared using data from the surface
stations) and a corresponding sequence of radar displays.
The surface maps
for 0900, 1200, 1500 and 1800 CST are shown in Fig. 5 -and the corresponding
radar displays in Fig. 6. The position of the leading edge of the squall
line on the surface maps was in part determined from radar data and in
part from the hourly time series at individual stations.
Most stations in Oklahoma reported overcast skies all day.
Prior
to 0800 CST none of the stations reported any thunderstorm activity.
surface map at 0900 CST is shown in Fig. 5a.
The
Ahead of the cold front temp-
eratures are near 65 deg F and winds generally from the south-southeast.
The one station behind the front has a temperature of 48 deg F and the wind
has shifted to northeast.
hour.
A thunderstorm was at this station in the past
The radar display at 0900 CST shows an intense echo northwest
(north being directed toward the top of the page) of NSSL near the left
edge of Fig. 6a which could have possibly been over the station in the
last hour.
The echoesat the western edge of the network did not progress
throu., it but moved north of it. In fact, none of the echoes which appear
on this display were associated with the squall line which later passed
through the network.
By 1200 CST four of the stations ahead of the front are reporting
thunderstorm activity.
Radar echoes are over the two stations which are
reporting thunderstorms at the time of observation.
Note that the echoes
ahead of the front (the average position of the surface front is indicated
by the straight line on the radar display) west of the mesonetwork are
not associated with the echoes that were slightly forward of this position
in Fig. 6a.
The latter echoes moved northward while the former moved
here from the south.
No distinct line of echoes has formed yet, however
the weak echoes, which are just entering the range of the radar westnorthwest of NSSL, are the beginnings of the line which passed through the
network.
In Fig. 5c is the surface analysis for -1500 CST.
The analysis shows
the development of a small surface wave and at the same time the radar
displays an organized squall line that is moving ahead of the surface cold
front.
The most intense part of the line, reflectivities as high as
62 dBz, is southwest of NSSL.
The squall line is well ahead of the front by 1800 CST and has
passe.d through the mesonetwork.
The front, along which no echoes are
now found, is just entering the western edge of the network.
So it appears that the squall-line thunderstorms did not appear
spontaneously in the warm air ahpad of the front but first appeared behind
it, formed a uniform squall line, and then moved out ahead of the front.
This kind of squall-line development is similar to that described by
Newton (1950).
Since the cold front moves with a speed nearly that of
12
low-level winds, and the air near the squall line derives its momentum
from higher levels where stronger winds prevail, it follows that the
squall line must move at a rate faster than the cold front.
4. Mesoscale situation and organization of data
As shown in the previous section a portion of the squall line migrated
through the NSSL mesonetwork between 1500 and 1800 CST.
Thus it was possi-
ble to attempt to study the mesoscale structure of the storm system.
The temperature traces, in general, displayed a dual temperature break.
A temperature break is defined here as the point on the trace at which the
temperature begins to fall sharply.
The first break, associated with the
leading edge of the cold air outflow from the line of thunderstorms (the
gust front), was very sharp.
Temperatures were near 66 deg F and dropped
to about 58 deg F in 10 min.
The second break, which occurred about 2 hours
later and was associated with cold-frontal-passage, was not as sharp as the
first and not clearly defined at all stations.
Shown in Fig. 7 are the temp-
erature and. rainfall traces recorded at surface station 2C.
The dual tempera-
ture break is apparent, and the onset of.rain begins about 5 min before the
first break.
Isochrones of the first temperature break and of the actual leading
edge of the radar echo line (defined here as a slightly smoothed line
centered between the first and second reflectivity contours at the leading
edge of the echo area) are presented in Fig. 8. It is interesting to
note that the break exhibits a curve-shaped pattern and it arrives in the
northern part of the network later than it does in the southern part.
At the same time, the leading edges of the radar echoes are more nearly
straight.
This structure is probably present because a strong southwesterly
flow, 35 m sec~,
is transporting the precipitation aloft, while a much
-
weaker flow near the surface, 10 m sec
-1
,
is transporting the cold air.
Isochrones of the arrival of the first westerly component in the
wind direction is shown in Fig. 9. The
in the temperature analysis is also here.
kind of pattern that was present
At most stations the shift in
the wind direction occurred a few minutes ahead of the first temperature
break.
Before the westward shift the winds were generally from the south-
southeast with speeds between 8 and 10 m sec~1.
After the shift the
stations in the northern portion of the network showed a decrease in
speeds, while the stations farther south showed an increase in speeds
followed by a decrease.
Cold-frontal passage at most stations was marked
by the appearance of a northerly component in the wind direction, which
cccurred some two hours after the appearance of the first westerly component.
Isochrones of the onset of rain are presented in Fig. 10.
The analysis
shows that the rain ran out ahead of both the temperature break and the
wind shift in the northern part of the network for the reason mentioned
above.
1969.
In Fig. 11 is the map of the total rainfall recorded on 26 April
The heaviest, 1.25 inches, was recorded at stations 7A and 6C in
the southwestern part of the network.
The most severe weather recorded
within the network occurred near this region.
Hail of up to 1.75 inches
in diameter was reported at Blanchard (BLA) around 1715 CST and a tornado
touched down near the Tabler community (see Fig. 11) about 1700 CST (U.S.
Department of Commerce, 1969).
The radar echo from a tornadic storm often displays a hook-shaped
appendage (Davies-Jones and Kessler, 1974).
this feature.
The Tabler tornado exhibits
The development of this hook echo as well as a brief history
of the squall line during the time it was within the surface network can
be summarized by viewing the half-hour interval sequence of PPI film
shown in Fig. 12.
At 1600 CST the line is entering the western edge of the network
and has an average width of about 35 km.
The most intense part of the
line, log Ze = 6.2, passes through the network.
As pointed out in Fig. 12a
the hook echo develops to the lower right of this high reflectivity region.
By 1630 CST the line has progressed over halfway through the network.
The northern part of the line has broken away from the main line.
place where the hook echo forms is again pointed out.
The
Fig. 12c shows
that the entire width of the line is within the network and has entered
into the ground clutter of the radar.
The hook-shaped appendage, on
the right of the most intense echo region, is clearly visible now and is
over the Tabler area.
The northern portion of the line has moved farther
away.
The arrangement of the radar echoes in a line as they passed through
the mesonetwork is apparent in all the above displays.
Isochrones of
the progress of the actual leading edge of radar echoes through the network are shown in Fig. 8. Since these lines are more nearly straight
than the isochrones of the temperature break and the wind shift we chose
to study this system in a frame of reference relative to the leading edges
of the radar echoes.
Here we define a smoothed average leading edge of
the radar echo line, hereafter referred to as LERE, as a straight line
moving at a constant speed of .53 km min1 , lying usually between the
first and second reflectivity contours.
Fig. 13 shows the advance of the
LERE line through the network and a coordinate system moving with the line.
A detailed explanation of this coordinate system is given in the Appendix.
The vertical structure of the storm system, as detected by radar,
was investigated by constructing vertical cross-sections from the PPI
echoes at elevated antenna-angles from 1 to 18 deg along azimuth 297
through station 5E.
A vertical cross-section was prepared for seven scans.
These sections were then composited into one.
An analysis was done on the
number of scans, out of the seven, which had non-zero reflectivity values
at a given point.
The 1- and 6-
lines taken from this analysis are
illustrated as dashed lines in Fig. 14.
The abscissa is labelled in
terms of both time and distance relative to the LERE.
The most intense
echo region extends from about 5 km ahead of to about 20 km behind the
LERE.
Also shown in Fig. 14 are the projections of the paths of the
rawinsonde balloons on the y(t) -p plane.
We found that with only 23 soundings.the data is too sparse to
permit the representation of significant meteorological variables (horizontal wind components, mixing ratio, and potential temp.erature) in all
three spatial dimensions and in time.
But the organization of the storm
system into a well-defined line and the short time span of the observational period suggest preparation of a composite analysis of the rawinsonde data based on the assumptions of a steady state and of no variation
in the direction parallel to the LERE.
Therefore, the variables were
analyzed and the results are presented in a vertical plane transverse to
the LERE.
However, lack of data prohibited the measurement of variations
in time, so it is not known whether the assumption of steady state is
valid.
Because of a strong south-southwesterly flow, the assumption of
no variations along the LERE is not valid in budget calculations.
Never-
theless, the results are still presented in a plane transverse to the LERE
since this presentation makes best use of the data.
In order to avoid inclusion of small irregularities in the analysis
of the rawinsonde data, 50-mb means of all pertinent meteorological variables are used, as suggested by Fankhauser (1974).
Note that the mean for
the lowest layer, from the- surface pressure to 950 mb, represents a
thickness of only about 9 mb.
mid-pressure of the layer.
These mean values are attributed to the
Details about the processing of the rawinsonde
data are described in the Appendix.
17
As shown in Fig. 14 of the five-attempts to launch a balloon in
the most intense echo region only one reached 400 mb.
A comparison of this
sounding with ones nearby showed that above 525 mb its rate of ascent,
mixing ratio, and equivalent-potential temperature were higher, indicating
it probably entered an active convective updraft above 525 mb.
The
crashes were either due to flight equipment failure or precipitation and
icing on the balloons.
This lack of data in the intense echo region
presented problems in the analysis that will be discussed later.
18
5. Distribution of meteorological variables
a. horizontal wind components.
The components of wind along the x and y axes of the coordinate
system shown in Fig. 13 are denoted by u and v, respectively.
Fig. 15 is the u component of the wind.
Shown in
Note the strong vertical shear
in a low-level jet-stream region near the surface.
While isolated
cumuli are often seen to be torn apart when subjected to strong vertical
shear, squall lines and large thunderstorms causing severe weather are
thought to show a preference for the jet-stream region where there is
strong vertical shear (Newton, 1963).
The field presents a strong south-southwesterly wind component
throughout the whole region except in the lower layers on the left, where
the strength has decreased somewhat.
In this respect this case differs
radically from the one studied by S & P, where the component of wind
along the front was quite small.
This strong south-southwesterly flow
is the main reason why the two-dimensional display in the y(t) - p plane
presented here cannot fully describe this three-dimensional system, that
is, advections - u
3Q
ax
are not negligible because of large values of u.
However, as stated before, because of spareness of data this type of
display makes the best use of it.
Through thermal wind considerations the temperature field was tested
to see if it supported the amount of vertical wind shear that existed in
the u field.
Individual point values did not show geostrophic agreement
but above 725 mb the amount of temperature change, averaged in y, required
by the wind shear was comparable to the observed temperature change across
the domain, thus indicating geostrophic agreement over the domain as a
whole.
But, on the average, between 875 and 725 mb the wind shear
required a temperature drop across the domain, while the observed temperatures increased.
Of course, in lower layers geostrophic agreement is
not expected because of the effects of surface friction, but here the
disagreement could also be due to suspect analyses in the region of very
little data.
The v component of the wind, relative to a moving frame of reference,
is presented in Fig. 16.
of the system.
875 up to 725 mb
Positive v values indicate motion to the rear
Along each pressure surface a maximum in v is present from
at -10 min.
Note that this maximum is at the right edge
of the most intense radar echoes, similar to the case of S & P.
Strong
convergence is noticeable from 0 to +40 min between 900 and 750 mb and
between 550 and 450 mb.
The west-northwesterly flow above 800 mb after
+30 min is noticeable in the tilt of the balloon trajectories shown in
Fig. 14.
Crude estimates of
3x
showed little systematic structure, leading
us to conclude that the pattern of vertical shear in Fig. 16 is almost
wholly ageostrophic.
b.
divergence and vertical wind component
For each of the twelve pressure layers between 959 and 400 mb the
divergence, D, was computed from
D
K
)
ax P
+
V)
,
KP
where u and v represent the average velocity component in the K layer
(not x-averaged) and p denotes reference to constant-pressure surfaces.
Note that here (only here) the derivative in the x direction is obtained
by use of finite difference methods over an interval of 10 km and not
by the method described in the Appendix.
The distribution of divergence
was averaged in x for each pressure layer and the resulting distribution
is shown in the y-p plane in Fig. 17.
Interesting features are the divergent-convergent doublet from -40
to +60 min below 600 mb and the convergent-divergent doublet from -40
to +80 min above 550 mb.
The divergent cores are due to divergence in
both the u and v fields.
The convergent areas are due primarily to the
strong convergence in v that was mentioned above.
To provide the divergence pattern at the surface,
au
an
were determined from 10-min averages of winds measured by surface stations
of the network.
nitudes of
Isopleths of u and v were drawn and from these the magand
ax
--
Dy
were determined over an interval of 8 km in
both the x and y directions.
is shown in Fig. 18.
The surface divergence pattern for 1640 CST
Convergence on the order of 10
-3
sec
-1.
is occurring
some 10 to 20 min ahead of the LERE and 10 to 20 min behind the actual
Judging from -pre-LERE soundings this is
leading edge of radar echoes.
a sufficient amount of convergence to provide the necessary lift to release
the potential instability and trigger convective activity over a matter
of minutes.
The divergence behind the 1640 CST LERE line is probably
due to downdraft from decaying radar cells.
The kinematic method of computing vertical velocities consists of
computing the divergence directly from the observed winds.
When the diver-
gence has been computed stepwise integration of the continuity equation
aw
ap,
+
D
=
0
K
(1)
yields the vertical component of velocity, w, at the top of all K layers:
K
W(x,yjpK
-
2Ap)
W(XYsPsfc) +
DK Ap
(2)
where Ap = 9 mb for K = 1 and 50 mb for all other K, and w(x. y, psfe,
the vertical motion at the surface,-is ignored in the calculation since
the w's computed aloft are much greater.
Now Fankhauser (1969) contends that the vertical velocity computed
from the kinematic technique produces reasonable values at low and
middle levels but diminishes in credibility in the upper layers.
He
attributes the decrease with height in the reliability of kinematic
vertical motion estimates to at least two facts.
First, the quality of
wind measurements from a GMD-l system (the type used at NSSL) deteriorates
with decreasing elevation angles, due to the combined consequence of
strong uniform winds aloft and sounding duration.
Second, as a result
of integrating (1), errors in the wind analysis in individual layers tend
to accumulate with height.
He suggests a scheme for the correction of
this problem which includes the assumption that w approaches zero at
100 mb.
In an effort to test the reliability of kinematically determined
vertical motions, &o,the average vertical motion over the domain from
-53.0 to +47.7 km was computed by the approximation
- (p)
where
u
--
=
P
/ sfc
p
v
is the average
_v-53 0)
100.7 km
4 7 7 (p)
au
dp
ax
'
for each y for each pressure level.
The
result of this computation is shown in Fig. 19.
Ascent reaches a maximum at,400 mb, the upper limit of the data.
Above this level it is not known if the profile will approach zero at
100 mb, so we cannot disprove Fankhauser's (1969) contention.
However,
since his results (see his Fig. 12) showed that significant adjustments
in the vertical motions were only necessary above 400 mb and since the
kinematically determined vertical motions of S & P were reasonable, we
are confident that our kinematically determined w's do not suffer greatly
from errors due to spurious divergences over deep layers.
The profile in Fig. 19 reveals an irregularity near 750 mb as in the
case of S & P.
The occurrence of this irregularity in both cases is
probably incidental.
Fig. 17 shows that the first impetus to upward
vertical motion below 800 mb is due to strong convergence over a large
region.
Above 650 mb the upward motion is given a second push by strong
convergence aloft.
This
entire portion of the updraft is believed to
be a result of condensational heating due to mesoscale ascent of saturated air triggered by the surface convergence discussed above, as in S & P.
The'vertical motion pattern, presented in Fig. 20, was calculated
from (2) at the top of all K layers and then averaged in x. The most prominent feature is the downdraft-updraft doublet between - 50 and +60 min,
the downdraft being centered at -20 min and the updraft centered at
+10 min.
S & P also found this same kind of doublet pattern in their
examination of a frontal disturbance.
Their region of descent was some-
what wider and the peak descent, which was somewhat stronger, occurred
near 400 mb.
An alternative analysis which was performed later on their
data reduced the magnitude of this descent by one-half, but it was still
about 40 x 10-3 mb sec
stronger than the peak descent shown in Fig. 20.
The occurrence of this downdraft-updraft doublet in two cases that were of
entirely different synoptic origin led to the search for other cases
which exhibited the same kind of mesoscale circulation pattern.
Fankhauser's (1974) vertical motions, obtained in his analysis of
a squall-line case, also showed a downdraft-updraft doublet.
The peak
upward and downward motions were somewhat weaker than the ones shown
- here.
On the basis of the results from these three cases one can tenta-
tively conclude that this type of mesoscale circulation exists in the
presence of severe storms during their mature stages whether they be of
frontal or squall-line character.
From the v field shown in Fig. 16 and the kinematically calculated
('s a streamfunction was calculated for motions in the y-p plane by
using the formulas,
ay
V
ap
Now T cannot accurately represent the flow since
au
an
ax
is not zero,
but it can portray either the w or v field correctly everywhere.
We
have chosen to represent the actual w's since we believe that the vertical
transports following the mean mesoscale motions are the most important
ones; this belief is supported in the budget calculations.
The v's at
-5.3 km were used as boundary conditions and T was arbitrarily set
equal to zero at 955 mb.
The streamfdnction lines of flow are shown as the dashed lines in
Fig. 21.
It is important to note that the streamfunction lines in the
lower layers do not show any upward motion between -20 and 0 min, where
we believe low-level convergence is responsible for triggering the convective activity.
Ascent is probably not visible because of the smoothing
and averaging processes that have been applied to the available data.
c. mixing ratio
An analysis of the mixing ratio following the procedure outlined
in the Appendix indicates relative humidities around 50 to 60% in the
location of most intense and persistent radar echoes.
This inconsistency
is attributable to lack of soundings in this region, where the air must
be saturated or very nearly so.
The analysis was adjusted in this
region to be consistent with the radar echoes, by accepting the temperature analysis as correct and by changing the mixing ratio values so that
the relative humidity in this region was 94%, a somewhat arbitrary value
that corresponds to the average value of relative humidity over all the
29 surface recording stations.
This value was taken as a lower limit of
what might be expected aloft.
The resulting field of mixing ratio, q, is shown in Fig. 21.
Note
that this adjustment tends to make the horizontal gradients near -20
and near +45 min extremely strong.
The strength of these gradients may
be excessive and they might yield spuriously strong sources and sinks
in the budget calculations.
The tight vertical gradient before -20 min
in the 850.to 750 mb layer is supported by individual soundings, especially
those launched in the southwestern part of the network prior to the arrival of the LERE, which showed a moist layer from the surface up to about
800 mb abruptly capped by a dry layer, which extended up to about 600 mb,
with another moist layer aloft.
The analysis shows these features.
Examination of individual soundings and surface observations indicates
that the upper moist layer prior to '-20 min represents a cloud deck of
altocumulus, mainly in the southwestern part of the network.
As for relative humidity, one dry region is intruding from the right
centered at 700 mb and another one is intruding from the left centered
near 525 mb as shown in Fig. 21.
The air is very moist near the surface
over the whole domain.
In Fig. 21 the streamfunction lines are superimposed on the q distribution to provide a visual impression of the rate of change of q
following the mean mesoscale motion in the y-p plane.
In the flow
through the system at lower levels prior to -40 min, q is on the average
conserved.
Elsewhere q decreases in regions of ascent and increases in
regions of descent (except in the region near the middle cloud deck
where q decreases in a region of descent, which seems to be a spurious
loss of moisture).
d.
equivalent-potential temperature
The equivalent-potential temperature, ee, was calculated for each
y at each pressure level using the formula
ae = 6 exp [ (Lq) / (C T) ]
where L is the latent heat of condensation, c
is the specific heat of
air at constant pressure, and T is the temperature.
The values of 0
and q shown in Figs. 21 and 23 were used in this calculation.
distribution appears in Fig. 22.
The 6e
The horizontal gradients near -20 and
+40 min may be too strong because of the adjustment made in the mixing
atio field.
Prior to -15 min Oe decreases from 900 mb up to a minimum
near 725 mb, indicating potential instability in this layer.
Above
there 6e increases upward until a maximum is reached near 575 mb, followed
again by a decrease in Oe up to 450 mb.
In.the principal mesoscale updraft region above 800 mb 0e decreases
upward to a minimum near 475 mb above which it increases.
may not really be as high as presented.
This minimum
The adjustment in q tended to
make the level of the minimum higher.
A qualitative look at the changes in e following the mean mesoscale
motion in the y-p plane shows 8e is.not conserved in most places.
Some
features are physically impossible to explain on the basis of this twodimensional flow; the u component must also be considered.
cannot be explained even then.
Some probably
These features are discussed in detail in
the section on budget calculations.
26
e. potential temperature
The field of potential temperature, e, appears in Fig. 23.
In
the lower layers up to 850 mb before -20 min the potential temperature
distribution is nearly horizontal.
After -70 min between 750 and 550 mb
the analysis shows a general cooling toward the west-northwest.
In general as the air moves through the system it is heated, however
for the air entering from the west-northwest at about 500 mb the value
of 0 at its entrance is higher than the value at its exift.
6. Mesoscale budgets
a. discussion of concepts
The main objective of this study is to determine the importance
of convection upon the heat, moisture, and momentum structure of the
mean mesoscale atmosphere.
These effects can be estimated as residuals
in budgets in which the transports by the mesoscale motions are explicitly
The approach to this problem is the same as that of S & P.
calculated.
The budget is considered for a quantity Q in a mesoscale volume 50 mb
deep, 10.6 .km in the y direction, and 30 km in the x direction.
The
overbar is used to indicate an average over such a volume and the prime
is used to indicate deviations from this average value.
The meteorologi-
cal variables presented in the previous section are synonymous with the
corresponding barred quantities presented in this section.
a0 X3y(UQ) +
at +
Q-
3
We have:
3p (WQ)
(VQ) +
(3)
+
a
-
(U Q1 ) +
where Q is the real source.
+
xy (Q
a
5p
+
WQ 1 )
The apparent source is denoted by
(UQ) +
p(Q),
(VQ) +
the rate of change following the mesoscale motion.
(4)
A virtual source,
denoted by
QV
-
a
(V1 Q1-) +
( 1Q1 ) +
a
Q )]
(5)
is assumed to essentially represent the effects of convective elements,
except in the surface boundary layer where the effects of surface friction
are included.
Rewriting (3) using (4) and (5)
Q
=Q
+
Q.
28
From the analysis of the mesoscale mean fields all the terms of Q
can be calculated except for
9t.
.*
We shall denote Q
and refer to it as the approximate apparent source.
and
--
can be determined only as residuals.
b.
equivalent-potential temperature
minus
3
*
as Q
The virtual source
The approximate apparent source of 0e is displayed in Fig. 24a.
- *
- v
Hence the apparent source of
Assuming adiabatic processes ee = 6e.
ee is due entirely to the virtual source, which is presumably associated
with convection.
In Fig. 24a, the large source region just prior to the LERE between
850 and 750 mb can perhaps be accounted for as a result of convective
elements transferring high
0e
from near the surface into this region.
But the magnitude of the corresponding sink is no more than .2 deg K min~,
Part of this discrepancy
while the source is as high as .8 deg R min-I.
is due to the spurious source which was introduced when the mixing ratio
field was adjusted.
If 0 e were reduced at lower levels near 0 min
the apparent sink would be larger.
The large sink near -20 min centered at 650 mb is physically impossible to explain on the basis of convection.
Its location is just above
a stable layer shown in the 6e field in Fig. 22.
A slight modification
in the Ue and T analysis making the contours parallel to the streamlines
in this region would eliminate part of this sink.
this loss is due to the change in
0e
Also a large part of
in the x direction.
Suppose that the local changes in the moving coordinate system
are just those produced by the u transport.
Then the apparent rates of
change are due entirely to the v and w transports.
two terms, for 6e, is shown in Fig. 24b.
The sum of these
The sink centered at -20 min
discussed above has been greatly reduced.
In both presentations convective
elements are transferring high values of 0e from below 475 mb to above
this level in the region of most intense radar echoes.
c.
potential temperature
In Fig. 25a is the approximate apparent source of 6. Apparent
heating and cooling are primarily taking place in regions of mesoscale
ascent and descent, respectively.
Before -10 min in the layer between
850 and 750 mb there is an apparent sink of 6 and source of 6e. It is
believed to be in this region that the initial cumulus convective clouds,
triggered by low-level convergence, were evaporating into the dry air
above 800 mb, thus accounting for the cooling here.
Above 650 mb the.
cooling is probably due to evaporation of the middle cloud deck entering
the southwestern part of the network.
These regions of cooling appear
to be driving the mesoscale downdraft.
In the main updraft region, where the air is nearly saturated on
the mesoscale, the apparent source is essentially a real source, latent
heat of condensation.
The effect of convection here is probably to ele-
vate the level of maximum heating.
Changes are on the order of .1 deg K min
with peak heating of .5 deg K min
over much of the system
and peak cooling of .3 deg K min
Exclusion of the u transport does not change the field much.
son of Figs. 25a and 25b shows that
-(u
ax
6)
.
A compari-
is not significant.
d. mixing ratio
The approximate apparent source of q is presented in Fig. 26a.
The source at -20 min centered near 800 mb is due to evaporation of cumulus convective clouds, which were initially set off by low-level convergence, into the dry air in middle levels.
The strength of this source
may be somewhat exaggerated, because of reasons mentioned earlier.
It
is accompanied by a much weaker sink below it. The source above 600 mb
near -20 min is due to evaporation of the cloud deck entering the southwestern part of the network.
The large loss of q in the region of mesoscale ascent between 0
It's not clear here what
and +60 min is due primarily to condensation.
the effect of convection is. The apparent loss between 700 and 600 mb
just prior to -20 min is not readily explained.
Part of it is due to
the u transport of q, which may be balanced by the local change of q.
In Fig. 26b is the approximate apparent source of q less the u transport.
The moisture loss between 700 and 600 mb before -20 min has been reduced
by one-half and the distribution is physically more pleasing.
The rainfall rate relative to the LERE appears in Fig. 27.
at the surface coincides the mesoscale updraft region.
Rain
The maximum rate
occurs at +20 min some 10 min after peak ascent is reached in this region.
e.
v - momentum
The equation of motion in the y direction can be written as
av.
-
+ u
aty
av
+-v
+ v
+
-av
3p
-
-
-
ay
- fu
(6)
(Wlvl)]
I (vivi) + ap
[ A
ax (ulvl) + 9y
where D is the geopotential on a constant-pressure surface.
The sum of
the terms on the left hand side of (6) represent the acceleration following
the mean mesoscale motion.
We shall refer to the sum of the last three
terms on the left as the approximate mesoscale acceleration.
The first
and second terms on the right hand side of (6) represent the pressure
gradient and coriolis forces, respectively.
The last three terms on the
right represent forces arising from surface friction and from internal
turbulent stresses (primarily convective).
The coriolis force and the approximate mesoscale acceleration were
determined from the mesoscale analysis.
The surface friction force was
parameterized in the lowest layer as
- Cd H
1 -cH
2
V(U
+
+
V2)
where Cd is a drag coefficient of 2 x 10-3, H is a layer of 200 meters,
and v was taken relative to the ground.
In Fig. 28 is the analysis of the coriolis force over the whole
domain and the parameterized surface friction force in the lowest layer.
Note that the coriolis force is considerable and always acts toward the
east-southeast.
In the lowest layer prior to +60 min the surface friction
and coriolis forces combine to act against the east-southeasterly flow.
Shown.in Fig. 29 are the approximate mesoscale accelerations.
Below 800 mb mesoscale accelerations are generally west-northwestward
before -10 min and east-southeastward after.
Figure 28 indicates that the
coriolis force is responsible for some of this east-southeastward acceleration.
Above 500 mb between -10 and +50 min strong accelerations toward
the west-northwest are present, despite opposing coriolis forces here.
These strong accelerations are due primarily to the rather abrupt
increase of v upwards, which was evident in individual soundings.
7. Concluding remarks
This study has examined the case of the 26 April 1969 squall line
which moved ahead of a surface cold front through the NSSL mesonetwork
in Oklahoma.
The squall-line system was within the NSSL mesonetwork about 2
hours and produced rain amounts up to 1.25 inches at some stations.
Hail with 1.75-inch diameter was recorded at one station in the southern
part of the network, and just outside NSSL the system spawned a tornado
which caused considerable damage.
This system can be regarded as severe.
It seems that the squall-line thunderstorms did not appear spontaneously in the warm air ahead of the front but first appeared behind
it, formed a uniform line, and then moved out ahead of the front.
Since the cold front moves with a speed close to that of the low-level
winds, and the air near the squall line derives its momentum from higher
levels, where stronger winds prevail, it follows that the squall line
must move at a rate faster than the surface cold front.
Although the analysis of the squall-line system was presented in
a two-dimensional display transverse to the leading edge of the radar
echoes to permit maximum use of the available data, the three-dimensional
characteristics of the system were evident in the surface and rawinsonde
observations.
The surface wind shift and temperature break associated
with the gust front revealed a curved-shaped pattern with the two events
arriving in the northern part of the network after the onset of precipitation.
Strong southwesterly flow did not justify the assumption of
small variations along the leading edge of the radar echo
line, so
crude estimates of these variations had to be made.
Despite the three-dimensional structure of the system, the two
33
dimensional display gave some interesting results.
the system appears to work as follows:
gust front) of the order of 10
sec
The mechanism of
surface convergence (due to the
first triggers convective activity.
An intense mesoscale downdraft-updraft doublet develops, the downdraft
b e i n-g
centered
about 10 km behind the leading edge of the radar
echoes and the updraft centered about 5 km ahead of it. Peak speeds in
the downdraft reach about 1.3 m sec~1 at 550 mb, while peak speeds in
the updraft reach about 2.5 m sec
at 400 mb.
These vertical currents
appear to be driven by a corresponding doublet of cooling and heating
with peak rates of .3 deg K per min of cooling and .5 deg K per min of
heating.
The cooling is produced by evaporation of initial convective
cloud tops in the dry air in middle layers and from the dissipation
of a middle cloud layer, and the heating is produced by latent heat
release due to condensation of water vapor along with the superimposed
convection.
This downdraft-updraft doublet is not only characteristic of this
case but of cases studied by Fankhauser (1974) and Sanders and Paine
(1975).
The synoptic situation was not the same in all three cases.
Two cases were squall-lines, while the convection resulted from frontal
over-running in the other.
On the basis of these studies it is tenta-
tively concluded that this doublet of mesoscale vertical motions may be
a distinguishing feature of large convective storm systems in their mature
stages, whether they be of frontal or squ'all-line character.
The lack of data prevented the complete analysis of the effect of
convective activity on the mean mesoscale atmosphere.
However convec-
tion plays an important role in providing the liquid water for evaporation and supplying some of the heating needed to drive the updraft and
cooling for the downdraft.
34
Future studies of this kind will require more soundings, both in
and out of storm areas.
Although Barnes (1974) suggests that no eco-
nomically feasible combination of rawinsondes will ever completely
resolve flow patterns and thermodynamic structure within severe storms,
rawinsondes are still the most reliable system for providing simultaneous
wind data at many vertical levels.
The dual-Doppler radar systems can
also be used to realize internal flow.
ACKNOWLEDGEMENTS
I am deeply indebted to Professor Frederick Sanders for introducing
me to the 26 April 1969 case, offering assistance and helpful discussions
throughout this research work, and spending time examining the rough
draft of this paper.
-
Thanks are extended to David Katz and Razia Ahmad
for their assistance in the initial preparation and analysis of the data,
Isabelle Kole for drafting the figures, and Virginia Mills for typing
the final draft.
Special thanks are due to my parents and friends for
their love and support.
APPENDIX
Fig. 13 shows the coordinate system used to process the rawinsonde
data.
The x axis is aligned with the mean LERE line and is assumed to
point 27 deg to the right of true north.
The positive y axis points
toward the rear of the system and passes through surface station 5E.
The origin of the system is assumed to lie on the mean LERE line and to
move with a velocity, V = -.53' km min
y direction.
1
,
j being
the unit vector in the
The t coordinate is defined to be coincident with the y
coordinate, by the relation t
=
y/.53.
Positive t values are defined
as the time since the LERE line passed the point located at y.
In order to determine the x, y, and t coordinates of the balloons
at'each
yressure
level the position of each of the 23 soundings was
plotted from its point of release up to-425 mb.
The t coordinate of the
balloon at any pressure level was determined by
t(p) = tR + tE -
t ERE ,
where tR is the release time of the balloon, tE is the elapsed time since
release of the balloon, and tLERE is the time the LERE line passed the
position of the balloon.
y = .53 t(p).
The y coordinate was determined by use of
The x coordinate was determined by measuring the distance
of the balloon from the y axis along a line parallel to the x axis.
Once the positions of the balloons were known for each pressure
layer the meteorological variables associated with these positions were
plotted in the x-y plane for the twelve pressure levels between 959 and
400 mb.
These horizontal charts were analyzed objectively and 286 data
points were determined for a rectangular area, with x ranging between
-20 and +40 km and y ranging between -58.3 and +53.0 km (t ranging
between -110 and +100 min).
The variables were then averaged in x to
give a y-p display of the significant meteorological variables.
Derivatives in the y and p directions were obtained by use of
finite difference methods.
The pressure interval is 50 mb while the
interval in the y direction is 10.6 km (or 20 min).
Derivatives of any
quantity in the x direction were obtained by dividing the rectangular
grid in half by a line parallel to the y axis, averaging the quantity in
x in each half of the grid for each y, assigning this average value to
the midpoint in each half section, and then using finite difference
methods over an interval of 30 km.
Unfortunately sparsity of data
prevented the measurement of local changes.
REFERENCES
Barnes, S. L., 1974:
1970.
Papers on Oklahoma thunderstorms, April 29-30,
NOAA TM ERL NSSL-69.
, J. H. Henderson, and R. J. Ketchum, 1971:
Rawinsonde
observation and processing techniques at the National Severe
Storms Laboratory.
Browning, K. A., 1964:
NOAA TM ERL NSSL-53.
Airflow and precipitation trajectories within
severe local storms which travel to the right of the winds.
J. Atmos. Sci., 21, 634-639.
Byers, H. R., 1974:
General Meteorology. New York:
McGraw-Hill Book
Co., 300-304.
Davies-Jones, R. and E. Kessler, 1974:
Tornadoes.Offprint from:
Weather and Climate Modification.
New York:
Dr. Wilmet N. Hess, editor.
John Wiley & Sons, Inc., 552-595.
Fankhauser, J. C., 1969:
Convective processes resolved by a mesoscale
rawinsonde network. J. Appl. Meteor., 8, 778-798.
,
1974:
The derivation of consistent fields of wind and
geopotential height from mesoscale rawinsonde data.
J. Appl.
Meteor., 13, 637-646.
Fawbush, E. J., R. C. Miller, and L. G. Starrett, 1951:
method of forecasting tornado development.
An empirical
Bull. Amer.
Meteor. Soc., 32, 1-9.
Lewis, J. M., Y. Ogura, and L. Gidel, 1974:
Large-scale influences
upon the generation of a mesoscale disturbance.
102, 545-560.
Mon. Wea. Rev.,
Newton, C. W., 1950:
line.
, 1963:
Structure and mechanism of the prefrontal squall
J. Meteor., 7, 210-222.
Dynamics of severe convective storms.
Meteor.
Monogr., 5, No. 27, 33-58.
Ogura, Y., and H. -R. Cho, 1973:
Diagnostic determination of cumulus
cloud populations from observed large-scale variables.
J. Atmos. Sci., 30, 1276-1286.
Sanders, F., and R. J. Paine, 1975:
The structure and thermodynamics
of intense mesoscale convective storm in Oklahoma.
J. Atmos.
Sci., 32, 1563-1579.
U.S. Department of Commerce, 1969:
Storm Data, 11, 33.
Yanai, M., S. Esbensen, and J. -H. Chu, 1973:
Determination of bulk
properties of tropical cloud clusters from large-scale heat
and moisture budgets.
Zittel, D.,
1976:
cation.
J. Atmos. Sci., 30, 611-627.
National Severe Storms Laboratory, Personal communi-
TABLE 1. WSR-57 Video Contour Levels and Equivalent Reflectivities
Level
Log Z e
Shading
1
2.04
Light Gray
2
2
3.20
Bright
3
3
4.23
Dark
4
4
5.18
Light Gray
5
5
6.20
Bright
6
Code
FIGURE LEGENDS
Fig. 1
The 1969 NSSL upper-air and surface mesonetwork.
Fig. 2
Synoptic situation at 0600 CST, 26 April 1969.
indicates location of NSSL mesonetwork.
Boxed area
(a) Surface map. Solid lines are isobars (mb) of sea-level
pressure; dashed lines are surface isotherms (0 C). -Front,
wind, cloud amount, and present weather phenomena are
indicated in standard synoptic notation.
(b) 400 mb chart. Solid lines are height contours
(decameters). Winds are indicated in standard synoptic
notation.
Fig. 3
Tinker Air Force Base temperature and dew-point soundings
on 26 April 1969. Winds are indicated in standard synoptic
notation, north pointing to top of diagram.
(a)
Soundings at 0600 CST
(b)
Soundings at 1800 CST
Fig. 4
Same as Fig. 2a but for 0600 CST, 27 April 1969.
line indicated by heavy dash-dotted line.
Fig. 5
Surface maps over the state of Oklahoma on 26 April 1969
at (a) 0900, (b) 1200, (c) 1500, and (d) 1800 CST. Dashedboxed area indicates location of NSSL mesonetwork. Solid
lines are isobars (mb) of sea-level pressure. Front, wind,
cloud amount, present weather phenomena, and instability line
are indicated in standard synoptic-scale notation. Temperatures are given in deg F.
Fig. 6
Radar PPI presentations at three-hour intervals on 26 April
1969. Labelled solid lines represent coded values
of log Ze,
the radar reflectivity factor at 0 deg elevation (see Table 1).
Area enclosed by dashed lines is NSSL mesonetwork. Straight
solid line is the average position of surface cold front.
Tick marks indicate portions of the echoes that have entered
the ground clutter of the radar.
Fig. 7
(a)
PPI presentation at 0900 CST
(b)
PPI presentation at 1200 CST
(c)
'PPI presentation
(d)
PPI presentation at 1800 CST
at
Instability
1500 CST
Temperature (OF) and rainfall (inches) traces recorded at
automatic surface recording station, 2C.
Fig. 8
Isochrones of first temperature break are solid lines.
Isochrones of leading edge of radar echoes are dashed
lines. Dash-dotted parts of dashed lines represent portions of the lines that have entered the ground clutter
of the radar. Dots and x's represent stations of mesonetwork as shown in Fig. 1. iAll times CST.
Fig. 9
Isochrones (CST) of first westerly component in wind
direction. Dots and x's as in Fig. 1.
Fig. 10
Isochrones (CST) of onset of rain.
in Fig. 1.
Fig. 11
Isohyets of total amount of rainfall (inches) on 26 April
1969. Dots and x's are as in Fig. 1.
Fig. 12
Radar PPI presentations at half-hour intervals on 26
April 1969. Labelled solid lines, area enclosed by
dashed lines, and tick marks are the same as in Fig. 6.
(a)
Dots and x's are as
PPI presentation at 1600 CST
(b) PPI presentation at 1630 CST
(c) PPI presentation at 1700 CST
Fig. 13
Isochrones (CST) of the LERE line (see text, section 4).
Radar PPI presentation at 0 deg elevation at 1650 CST.
Intensity levels 1 and 4 are shown. A coordinate system
moving with the line is on the right. Area enclosed by
dashed lines is as in Fig. 6.
Fig. 14
Projections of paths of the rawinsonde balloons in the
y(t)-p plane. Dots represent positions of individual
balloons at surface and 50-mb intervals. Dashed lines
enclose radar echo region.. Abscissor labelled in time
and distance relative to the LERE line.
Fig. 15
u component of wind (m sec~ ) with respect to a fixed
coordinate system. Positive values for air moving into
the page.
Fig. 16
v component of wind (m sec~ ) with respect to a moving
coordinate system. Positive.values for air moving toward
the left.
Fig. 17
Divergence of the horizontal wind field, labelled in
units of 10-5 sec-l'
Fig. 18
Surface divergence pattern at 1640 CST. Solid lines
labelled in units of 10~4 sec- 1 . Dashed lines are isochrones of the LERE line. The actual leading edge of
radar echoes at 1640 CST is indicated by the thin solid
line. Dots and x's are as in Fig. 1.
-3
-l
mb sec
Fig. 19
Profile of domain-averaged vertical motion, w(10
Fig. 20
-l
~ -3
mb sec ) derived from
Mesoscale vertical motions ol(10
conventional kineibatic technique.
Fig. 21
Dashed lines are
Mesoscale mixing ratio, q4 (g Kg 1
streamfunction lines of flow relative to the LERE line at
intervals of 400 mb m sec-1 . Hatching and stippling
represent, respectively, areas of relative humidity less
than 25% and greater than 75%.
Fig. 22
Mesoscale equivalent-potential temperature, Oe(deg K).
Streamfunction lines are as in Fig. 21.
Fig. 23
Mesoscale potential temperature, O(deg K).
lines are as in Fig. 21.
Fig. 24
(a) Approximag apparent source of equivalent-potential
temperature, 6e , labelled in units of 10-2 deg K min 1 .
Streamfunction
(b) Approximate apparent source of equivalent-potential
temperature minus u transport, labelled in units of
10~ deg K min-1 .
-**
Fig. 25
-
(a)
Same as Fig. 24a except for potential temperature, 6
(b)
Same as Fig. 24b except for potential temperature.
.**
Fig. 26
(a) Approximate apparent source of mixing ratio, q
labelled in units 10-2 gm Kg- 1 min- 1 .
(b) Approximate apparent source of mixing ratio minus u
transport, labelled in units of 10-2 gm Kg-1 min- 1 .
Fig. 27
Measured surface rainfall rate in units of centimeters
per 10 minutes.
Fig. 28
The coriolis force plus the parameterized surface friction
force (in the lowest layer) per unit mass, labelled in
units of 10-3 m sec- 2 .
Fig. 29
Approximate mesoscale v-accelerations labelled in units
of 10-3 m sec- 2 .
).
Fig.
I
5
%
|006
.
9 QE
996
0085
0%w
I )08
~
>21004
004--10
Oe
1006
012 ~
1000
100
100
10040
Fig.
2a
060OCST
APRIL 26 1969
N
N
N
0-74
746-
/00
Fig. 2b
0600CST
APRIL 26 1969
P (mb)
400r
T (*C)
Fig.
3a
P(mb)
-30
-20
0
-to
T (*C)
Fig.
3b
10
Fig.
4
1200CST
April 26, 1969
0900 CST
April 26. 1969
~3595
351
/
(b)-
1
oop
+35.
95
1oo2
1004
1500CST
April /26,1969
(c)
Fig. 5
/
1002
I800CST
-,April 26,1969
(d)
.4'e.-32 >J 2
I
I
I
I
I
-v
NSS L
43
0
Fig.
6a
20
40
60 KM
a,,
p In_
tO
W
'NI
(Oy~
~
0 20
Fig.
6b
-,NSSL
'-p
40
60 KM
)
%2
/
I
I
'~'NSSL
o
Fig. 6c
20
40
60KM
%
-NSSLc
II
I3
S
4
44
43
4~
Fig. 6d
-40
60 KM
CST
t-n
I
I $
I
\lvv;cl
1559
N
3
Fig. 7
It
la-
45
1859 CST
t859 CST
17 5 9
9
17
1659
k
6
7
1640
170 0
1720
1730
I g
i
/
/
/
/,
/
/
,
/
10
Fig. 8
,
20KM
1710
/
1720
/ 1730
0
Fig.
9
10
20KM
Fig. 10
/
/
*
Tobler
o
Fig.
11
10
20 KM
60
9
1'
2
'3,
ONSSL
ho
develops
here
0
20
a
i
Fig. 12a
40
60 KM
NSSL
--V.
hook
develops
here
.
n
a
Fig.
12b
20
40
60KM
24
-
'NSSL
Hook
o
I-
Fig. 12c
-
20',I
40
60KM
0'
1530 1600 1630 1700 1730 1800 CST
2
I
20
Fig.
13
-
I
40
I
60 KM
-
001I I 1111
091 1
I
/
X
09/ I I I I /
I I
Ot'/ I
1 1
021/ I / I /
(V'J
))
9101
(Ni00o)
0
I I
0t
I I I / i I /
I I I
/
8*12
09
/ I
/
II
' I.
T
*1 -4:
Vt?*Z
001
08
L/ / /,/L/ I
926
I
I
\...\\...
..
\
.1
Al
.I.....
\X' *V
..
1....:..
I A0 \A\ *i ...
....
I...
....
iIL
I\I ...
Ilk
Ii~
I
i:
\i&.....I...
111
........
6~
g99
&
A
R
A
0~
-I
-D
94L9
/
I.II
I~IX I;I I;
*11'
~
I......../
.-
. .
..
....
6111!
\I
P(mb)
400r
24
800-
28
900 -
8
16 2
I
1000,
100
53.0
Fig.
15
80
60
40
42.4
31.8
21.2
I
0
-20
Time (min)
-10.6
0.0
10.6
Distance (kim)
20
I
I
-40
-60
-80
-21.2
-31.8
-424
-100
-53.0
P(rrb)
400 t-
8
P,
16
0
-6
---
80
60
40
0
20
Time
53.0
Fig. 16
424
31.8
212
106
-40
-60
-80
-100
-10.6
-21.2
-318
-424
-53.0
(min)
0.O
Distance
-20
(km)
P(mb)
400r
-0
800
60
80
000
53.0
Fig. 17
0
80
60
40
42.4
31.8
21.2
0
0
T2m
-20
0
T ime (min)
-10.6
0.0
10.6
Distance (kin)
20
-40
-60
-80
-100
-21.2
-31.8
-42.4
-53.0
68
1700
1640
1620
/x/
x
//-5
//
5-5
/
/o
x
-10
5/
-(
-10/
-1
/
|
10 20 K
Fig--518
O0
Fig.
/
20 Kx
P(mb
)
I
I
i
I
I
400-
5001-
6001S
700-
800-
K
0
9001-
10001
-3 6
Fig.
19
p
-32
p
-28
I
-24
-20
-16
0 ( 0 3 mbsec~)
I
-12
I
-8
-4
0
P(mb)
40
53.0
Fig. 20
42.4
31.8
21.2
-20
0
Time (min)
10.6
0.0
-10.6
Distance (km) '
20
-40
-21.2
-31.8
.-42.4
-53.0
P(mb)
50
-
)OO
10O
80
53.0
40....
..
60...
4.2.4
31.8
21.2
0
Time.(min)
20
-4
10~......-6-2..-.8
Distnce
Fig. 21
-2.-0.60-8.-0
..
(km
.
-5
.
P(mb)
-
400
24
4 #
1
500-
320
60 0
32
-241322
-3
18
-
\\3
/
%"%
iI........
......
328
%
32320
0-3263
60
-4
318
/
2 4 3 2i"
1316
314
800
32 2
20
40
232
33
330
900"--- 330
320
Fig3
222
10 0
s0
60
40
20
53.0
42.4
31.8
21.2
10.6
Tie0 (i)-20
0.0
-10.6
Distance (km)
Fig. 22
-40
- 60
-80
-21.2
-31.8
- 42.4
-t00
-53.0
P (mb)
400r-
100
80
60
40
20
53.0
42.4
31.8
21.2
10.6
Fig. 23
T ime
0
0.0
(min)
-20
-40
-60
-80
-10.6
-21.2
-31.8
-42.4
Distance (km)
-100
-53.0
400
500
600
E700
k..O
10L
800
900
1000
100
80
60
40
53.0
42.4
31.8
21.2
Fig. 24a
20
0
(MIN.)
0.0
10.6
(KM)
-20
-40
-60
-80
-100
-10.6
-21.2
-31.8
-42.4
-53.0
P (mb
40 0
)
1
0
500 (0)
0
600k
C
20
20
700k \
80 0-
0
- 20
9001i
f
10001
IC0
53.0
r r r 7 7 r f r 7 11f r 7 1 1 -- f 1 , f f I I 'I 1 1 r / f f f
80
42.4
60
40
20
31 8
21.2
10.6
Time
r rI
f
I
r
r
f
f
f
l
f f
f
f
9
I
-20
-40
-40
-60
-60
-80
-100
(min)
10.6
0.0
-21.2
- 31.8
-424
-53.0
0
-20
Distance (km)
Fig. 24b
/ 1 1 f 1 1
-80
-100
I
400
I
I
I
r
I
I
100
80
60
I
I
I
I
I
I
I
500
600
.D
0.
700h
800
90011000
53.0
Fig. 25a
42.4
31.8
I
-20
40
20
21.2
(MIN.)
0.0 -10.6
10.6
(K M)
-40
-60
-80
-21.2
--31.8
-42.4
-100
-53.0
P(mb)
4001
5001-
-20
0
600k
10
0
700k
10
-10
'-4
'-4
800 k
900
~,1
1000-100
53.0
Fig. 25b
I
III
80
60
40
20
42.4
31.8
21.2
10.6
I
0
-20
Time (min)
0.0
-10.6
Distance (km)
I
II
-40
-60
-21.2
-31.8
-
-80
-100
-42.4
-53.0
4001
500600E 700
O
800900
//0/
I100OO
53.0
Fig. 26a
/ / /0
/ /
80
60
40
42.4
31.8
212
.
0
(MIN.)
0.0
10.6
(KM)
20
-100
-20
-40
-60
-80
-10.6
-21.2
-31.8
-424 -53.( )
P(mb)
400r
500-
0 --. ... ...
600
10
700-
O
8001-
900I
'(00-'
100
80
53.0
Fig.
26b
42.4
7
'
60
40
20
31.8
21.2
10.6
0
-
I
-20
Time (min)
-10.6
0.0
Distance (km)
/
I
1
-40
-21.2
-60
-31.8
-80
-100
-42.4
-53.0
-i
.00-
.25
0
E .50-
000
0.
C
.75
1.00
100
Fig. 27
80
60
40
20
-20
0
Time (min)
-40
-60
-80
-100
P(mb)
4001
500F-
-3.0
600k
-2.5
700-
-2.0
Co
800M'-1.5
9001-
-2.5
-0.51
I
(OOOL
p
100
80
60
40
53.0
424
31.8
21.2
Fig. 28
I
I
I
0
-20
Time (min)
10.6
0.0
-10.6
Distance (km)
.20
I
I
I
I
-40
-60
-80
-100
-21.2
-31.8
-424
-53.0
P(mb)
400
15
500r-
10
.
0
600
C 5D
7001kC)
800k-
C
C
900-
i000OI
100
53.0
Fig. 29
.
I
I
80
60
40
42.4
31.8
21.2
I
-20
0
Time (min)
0.0
-10.6
106
Distance (km)
20
-40
-60
-80
-100
-21.2
-31.8
-42.4
-53.0